Cycles containing all vertices of maximum degree

For a graph G and an integer k, denote by Vk the set {v ε V(G) | d(v) ≥ k}. Veldman proved that if G is a 2-connected graph of order n with n ≤ 3k - 2 and |Vk| ≤ k, then G has a cycle containing all vertices of Vk. It is shown that the upper bound k on |Vk| is close to best possible in general. For the special case k = δ(G), it is conjectured that the condition |Vk| ≤ k can be omitted. Using a variation of Woodall's Hopping Lemma, the conjecture is proved under the additional condition that n ≤ 2δ(G) + δ(G) + 1. This result is an almost-generalization of Jackson's Theorem that every 2-connected k-regular graph of order n with n ≤ 3k is hamiltonian. An alternative proof of an extension of Jackson's Theorem is also presented

Optical Evidence of Multiphase Coexistence in Single Crystalline (La,Pr,Ca)MnO3

We investigated temperature (T)- and magnetic field-dependent optical conductivity spectra (\s\w) of a La_5/8-yPr_yCa_3/8MnO_3 (y~0.35) single crystal, showing intriguing phase coexistence at low T. At T_C < T < T_CO, a dominant charge-ordered phase produces a large optical gap energy of ~0.4 eV. At T < T_C, at least two absorption bands newly emerge below 0.4 eV. Analyses of (\s\w) indicate that the new bands should be attributed to a ferromagnetic metallic and a charge-disordered phase that coexist with the charge-ordered phase. This optical study clearly shows that La_5/8-yPrCa_3/8MnO_3 (y~0.35) is composed of multiphases that might have different lattice strains.Comment: A single file with 9 figures embedded, to appear in Phys. Rev.

Dimensional Crossover driven by Magnetic Ordering in Optical Conductivity of Pr_{1/2}Sr_{1/2}MnO_3

We investigated optical properties of Pr_{0.5}Sr_{0.5}MnO_3, which has the A-type antiferromagnetic ordering at a low temperature. We found that T- dependence of spectral weight transfer shows a clear correlation with the magnetic phase transition. In comparison with the optical conductivity results of Nd_{0.5}Sr_{0.5}MnO_3, which has the CE-type antiferromagnetic charge ordering, we showed that optical properties of Pr_{0.5}Sr_{0.5}MnO_3 near the Neel temperature could be explained by a crossover from 3D to 2D metals. Details of spectral weight changes are consistent with the polaron picture.Comment: 11 pages, 4 figures, submitted to PRL at June

Melting of Charge/Orbital Ordered States in Nd1/2_{1/2}Sr1/2_{1/2}MnO3_3: Temperature and Magnetic Field Dependent Optical Studies

We investigated the temperature ($T=$ 15 $\sim$ 290 K) and the magnetic field ($H=$ 0 $\sim$ 17 T) dependent optical conductivity spectra of a charge/orbital ordered manganite, Nd$_{1/2}$Sr$_{1/2}$MnO$_3$. With variation of $T$ and $H$, large spectral weight changes were observed up to 4.0 eV. These spectral weight changes could be explained using the polaron picture. Interestingly, our results suggested that some local ordered state might remain above the charge ordering temperature, and that the charge/orbital melted state at a high magnetic field (i.e. at $H=$ 17 T and $$ 4.2 K) should be a three dimensional ferromagnetic metal. We also investigated the first order phase transition from the charge/orbital ordered state to ferromagnetic metallic state using the $T$- and $H$% -dependent dielectric constants $\epsilon_1$. In the charge/orbital ordered insulating state, $\epsilon_1$ was positive and $d\epsilon_1/d\omega \approx 0$. With increasing $T$ and $H$, $\epsilon_1$ was increased up to the insulator-metal phase boundaries. And then, $\epsilon_1$ abruptly changed into negative and $d\epsilon_1/d\omega >0$, which was consistent with typical responses of a metal. Through the analysis of $\epsilon_1$ using an effective medium approximation, we found that the melting of charge/orbital ordered states should occur through the percolation of ferromagnetic metal domains.Comment: submitted to Phys. Rev.

The in vitro effects of dehydroepiandrosterone on human osteoarthritic chondrocytes

AbstractObjective: To investigate the in vitro effects of dehydroepiandrosterone (DHEA) on human osteoarthritic chondrocytes.Design: Chondrocytes isolated from human osteoarthritic knee cartilage were three-dimensionally cultured in alginate beads, except for cell proliferation experiment. Cells were treated with DHEA in the presence or absence of IL-1β. The effects on chondrocytes were analyzed using a 3-(4,5-dimethylthiazol-2yl)-5-(3-carboxymethoxy-phenyl)-2-(4-sulfophenyl)-2H-tetrazolium inner salt (MTS) assay (for chondrocyte proliferation), a dimethylmethylene blue (DMB) assay (for glycosaminoglycan (GAG) synthesis), and an indole assay (for DNA amount). Gene expressions of type I and II collagen, metalloproteinase-1 and -3 (MMP-1 and -3), and tissue inhibitor of metalloproteinase-1 (TIMP-1) as well as the IL-1β-induced gene expressions of MMP-1 and -3 were analyzed by reverse transcription-polymerase chain reaction (RT-PCR). The protein synthesis of MMP-1 and -3 and TIMP-1 was determined by Western blotting.Results: The treatment of chondrocytes with DHEA did not affect chondrocyte proliferation or GAG synthesis up to 100μM of concentration. The gene expression of type II collagen increased in a dose-dependent manner, while that of type I decreased. DHEA suppressed the expression of MMP-1 significantly at concentrations exceeding 50μM. The gene expression of MMP-3 was also suppressed, but this was without statistical significance. The expression of TIMP-1 was significantly increased by DHEA at concentrations exceeding 10μM. The effects of DHEA on the gene expressions of MMP-1 and -3 were more prominent in the presence of IL-1β, in which DHEA suppressed not only MMP-1, but also MMP-3 at the lower concentrations, 10 and 50μM, respectively. Western blotting results were in agreement with RT-PCR, which indicates that DHEA acts at the gene transcription level.Conclusions: Our study demonstrates that DHEA has no toxic effect on chondrocytes up to 100μM of concentration and has an ability to modulate the imbalance between MMPs and TIMP-1 during OA at the transcription level, which suggest that it has a protective role against articular cartilage loss

Reversible magnetization of MgB2 single crystals with a two-gap nature

We present reversible magnetization measurements on MgB2 single crystals in magnetic fields up to 2.5 T applied parallel to the crystal's c-axis. This magnetization is analyzed in terms of the Hao-Clem model, and various superconducting parameters, such as the critical fields [Hc(0) and Hc2(0)], the characteristic lengths [xi(0) and lambda(0)], and the Ginzburg-Landau parameter, kappa, are derived. The temperature dependence of the magnetic penetration depth, lambda(T), obtained from the Hao-Clem analysis could not be explained by theories assuming a single gap. Our data are well described by using a two-gap model.Comment: 20 pages, 1 table, 4 figures, will be published in Phys. Rev.

Comparison of computed tomographic findings in pulmonary mucormycosis and invasive pulmonary aspergillosis

AbstractBecause there are no available molecular markers for pulmonary mucormycosis (PM), which has low culture sensitivity, early diagnosis and treatment rely heavily on imaging modes such as computed tomography (CT). However, there are limited data comparing CT findings for PM with those for invasive pulmonary aspergillosis (IPA). Adult patients who met the modified criteria for proven and probable PM (over an 11-year period) and IPA (over a 6-year period, owing to the availability of the galactomannan assay) according to the modified European Organization for Research and Treatment of Cancer/Mycosis Study Group definitions were retrospectively enrolled. IPA cases were selected at a 1 : 4 (PM/IPA) ratio. Thoracic CT scans were reviewed by two experienced radiologists blinded to the patients' demographics and clinical outcomes. A total of 24 patients with PM, including 20 (83%) with proven PM and four (17%) with probable PM, and 96 patients with IPA, including 12 (13%) with proven IPA and 84 (87%) with probable IPA, were eventually analysed. The reverse halo sign was more common in patients with PM (54%) than in those with IPA (6%, p < 0.001), whereas some airway-invasive features, such as clusters of centrilobular nodules, peribronchial consolidations, and bronchial wall thickening, were more common in patients with IPA (IPA 52% vs. PM 29%, p 0.04; IPA 49% vs. PM 21%, p 0.01; IPA 34% vs. PM 4%, p 0.003, respectively). The reverse halo sign was more common, and airway-invasive features were less common, in patients with PM than in those with IPA. These findings may help physicians to initiate Zygomycetes-active antifungal treatment earlier

Photon Statistics; Nonlinear Spectroscopy of Single Quantum Systems

A unified description of multitime correlation functions, nonlinear response functions, and quantum measurements is developed using a common generating function which allows a direct comparison of their information content. A general formal expression for photon counting statistics from single quantum objects is derived in terms of Liouville space correlation functions of the material system by making a single assumption that spontaneous emission is described by a master equation